MinT - Best Known (223−118, 223, s)-Nets in Base 4

Best Known (223−118, 223, s)-Nets in Base 4

(223−118, 223, 130)-Net over F₄ — Constructive and digital

Digital (105, 223, 130)-net over F₄, using

net from sequence [i] based on digital (105, 129)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
  - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(223−118, 223, 144)-Net over F₄ — Digital

Digital (105, 223, 144)-net over F₄, using

t-expansion [i] based on digital (91, 223, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(223−118, 223, 1386)-Net in Base 4 — Upper bound on s

There is no (105, 223, 1387)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 183 329572 096208 604138 493620 048788 369405 372077 405333 992101 989272 179447 909746 163941 253903 843164 224271 999237 567423 764202 564096 808019 386800 > 4²²³ [i]