MinT - Best Known (79−31, 79, s)-Nets in Base 4

Best Known (79−31, 79, s)-Nets in Base 4

(79−31, 79, 130)-Net over F₄ — Constructive and digital

Digital (48, 79, 130)-net over F₄, using

5 times m-reduction [i] based on digital (48, 84, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 42, 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]

(79−31, 79, 146)-Net over F₄ — Digital

Digital (48, 79, 146)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(79−31, 79, 2881)-Net in Base 4 — Upper bound on s

There is no (48, 79, 2882)-net in base 4, because

1 times m-reduction [i] would yield (48, 78, 2882)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 91781 181353 401806 059654 820108 887712 793576 505248 > 4⁷⁸ [i]