MinT - Best Known (204−83, 204, s)-Nets in Base 4

Best Known (204−83, 204, s)-Nets in Base 4

(204−83, 204, 130)-Net over F₄ — Constructive and digital

Digital (121, 204, 130)-net over F₄, using

t-expansion [i] based on digital (105, 204, 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]

(204−83, 204, 281)-Net over F₄ — Digital

Digital (121, 204, 281)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−83, 204, 5115)-Net in Base 4 — Upper bound on s

There is no (121, 204, 5116)-net in base 4, because

1 times m-reduction [i] would yield (121, 203, 5116)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 166 033485 951678 165832 011521 756934 479714 962266 163223 804240 925311 010810 388317 566730 624734 624763 578977 079616 758676 072814 369843 > 4²⁰³ [i]