MinT - Best Known (109, 109+67, s)-Nets in Base 4

Best Known (109, 109+67, s)-Nets in Base 4

(109, 109+67, 130)-Net over F₄ — Constructive and digital

Digital (109, 176, 130)-net over F₄, using

t-expansion [i] based on digital (105, 176, 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]

(109, 109+67, 309)-Net over F₄ — Digital

Digital (109, 176, 309)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+67, 6811)-Net in Base 4 — Upper bound on s

There is no (109, 176, 6812)-net in base 4, because

1 times m-reduction [i] would yield (109, 175, 6812)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2296 074761 448043 597427 172877 133517 800584 511230 800247 991395 725492 762824 765557 025851 111697 938202 893725 450340 > 4¹⁷⁵ [i]