MinT - Best Known (82, 82+37, s)-Nets in Base 4

Best Known (82, 82+37, s)-Nets in Base 4

(82, 82+37, 240)-Net over F₄ — Constructive and digital

Digital (82, 119, 240)-net over F₄, using

t-expansion [i] based on digital (81, 119, 240)-net over F₄, using
- 1 times m-reduction [i] based on digital (81, 120, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 40, 80)-net over F₆₄, using
    - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]

(82, 82+37, 472)-Net over F₄ — Digital

Digital (82, 119, 472)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+37, 22261)-Net in Base 4 — Upper bound on s

There is no (82, 119, 22262)-net in base 4, because

1 times m-reduction [i] would yield (82, 118, 22262)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 110429 602908 427605 859214 847188 911391 869862 225311 611230 975747 968045 673710 > 4¹¹⁸ [i]