MinT - Best Known (227−99, 227, s)-Nets in Base 4

Best Known (227−99, 227, s)-Nets in Base 4

(227−99, 227, 130)-Net over F₄ — Constructive and digital

Digital (128, 227, 130)-net over F₄, using

t-expansion [i] based on digital (105, 227, 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]

(227−99, 227, 247)-Net over F₄ — Digital

Digital (128, 227, 247)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−99, 227, 3770)-Net in Base 4 — Upper bound on s

There is no (128, 227, 3771)-net in base 4, because

1 times m-reduction [i] would yield (128, 226, 3771)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11660 019848 322269 697851 303352 872738 351327 221795 993218 267609 446038 718432 129577 490849 609531 848307 442657 763014 194720 315533 659688 333340 769854 > 4²²⁶ [i]