MinT - Best Known (157−98, 157, s)-Nets in Base 4

Best Known (157−98, 157, s)-Nets in Base 4

(157−98, 157, 66)-Net over F₄ — Constructive and digital

Digital (59, 157, 66)-net over F₄, using

t-expansion [i] based on digital (49, 157, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(157−98, 157, 91)-Net over F₄ — Digital

Digital (59, 157, 91)-net over F₄, using

t-expansion [i] based on digital (50, 157, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(157−98, 157, 501)-Net in Base 4 — Upper bound on s

There is no (59, 157, 502)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 33916 051774 855762 735504 254398 892263 342935 893839 935531 137645 907177 888154 920210 980663 130794 289801 > 4¹⁵⁷ [i]