MinT - Best Known (221−99, 221, s)-Nets in Base 4

Best Known (221−99, 221, s)-Nets in Base 4

(221−99, 221, 130)-Net over F₄ — Constructive and digital

Digital (122, 221, 130)-net over F₄, using

t-expansion [i] based on digital (105, 221, 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]

(221−99, 221, 222)-Net over F₄ — Digital

Digital (122, 221, 222)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−99, 221, 3175)-Net in Base 4 — Upper bound on s

There is no (122, 221, 3176)-net in base 4, because

1 times m-reduction [i] would yield (122, 220, 3176)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 846136 735194 973688 098655 955025 881277 078382 029485 590038 067992 426624 755315 016105 553592 278492 624716 558201 344376 269205 654466 114889 162380 > 4²²⁰ [i]