MinT - Best Known (90, 90+46, s)-Nets in Base 4

Best Known (90, 90+46, s)-Nets in Base 4

(90, 90+46, 152)-Net over F₄ — Constructive and digital

Digital (90, 136, 152)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (9, 32, 22)-net over F₄, using
  - net from sequence [i] based on digital (9, 21)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 22, using
      - an explicitly constructive algebraic function field [i]
2. digital (58, 104, 130)-net over F₄, using
  - trace code for nets [i] based on digital (6, 52, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(90, 90+46, 196)-Net in Base 4 — Constructive

(90, 136, 196)-net in base 4, using

2 times m-reduction [i] based on (90, 138, 196)-net in base 4, using
- trace code for nets [i] based on (21, 69, 98)-net in base 16, using
  - 1 times m-reduction [i] based on (21, 70, 98)-net in base 16, using
    - base change [i] based on digital (7, 56, 98)-net over F₃₂, using
      - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
        a function field by SÃ©mirat [i]

(90, 90+46, 376)-Net over F₄ — Digital

Digital (90, 136, 376)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+46, 11392)-Net in Base 4 — Upper bound on s

There is no (90, 136, 11393)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7591 243262 562989 647153 260595 295223 014938 849317 617427 226944 493913 022485 039161 993600 > 4¹³⁶ [i]