MinT - Best Known (191−132, 191, s)-Nets in Base 4

Best Known (191−132, 191, s)-Nets in Base 4

(191−132, 191, 66)-Net over F₄ — Constructive and digital

Digital (59, 191, 66)-net over F₄, using

t-expansion [i] based on digital (49, 191, 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]

(191−132, 191, 91)-Net over F₄ — Digital

Digital (59, 191, 91)-net over F₄, using

t-expansion [i] based on digital (50, 191, 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]

(191−132, 191, 415)-Net in Base 4 — Upper bound on s

There is no (59, 191, 416)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 082200 574837 072864 318735 334023 554157 284190 419768 128129 388313 797430 088467 346110 249082 583878 245958 516403 212148 415050 > 4¹⁹¹ [i]