MinT - Best Known (157−59, 157, s)-Nets in Base 4

Best Known (157−59, 157, s)-Nets in Base 4

(157−59, 157, 130)-Net over F₄ — Constructive and digital

Digital (98, 157, 130)-net over F₄, using

27 times m-reduction [i] based on digital (98, 184, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 92, 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]

(157−59, 157, 294)-Net over F₄ — Digital

Digital (98, 157, 294)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−59, 157, 6716)-Net in Base 4 — Upper bound on s

There is no (98, 157, 6717)-net in base 4, because

1 times m-reduction [i] would yield (98, 156, 6717)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8361 816773 277124 304224 230909 886117 692969 562419 309428 992715 135492 091811 383565 936062 053761 387132 > 4¹⁵⁶ [i]