MinT - Best Known (101, 180, s)-Nets in Base 4

Best Known (101, 180, s)-Nets in Base 4

(101, 180, 130)-Net over F₄ — Constructive and digital

Digital (101, 180, 130)-net over F₄, using

10 times m-reduction [i] based on digital (101, 190, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 95, 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]

(101, 180, 198)-Net over F₄ — Digital

Digital (101, 180, 198)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 180, 2943)-Net in Base 4 — Upper bound on s

There is no (101, 180, 2944)-net in base 4, because

1 times m-reduction [i] would yield (101, 179, 2944)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 587599 366842 666915 619060 558367 435322 278733 881392 733944 472010 459814 595852 277693 037457 777208 231365 409446 094445 > 4¹⁷⁹ [i]