MinT - Best Known (109, 109+71, s)-Nets in Base 4

Best Known (109, 109+71, s)-Nets in Base 4

(109, 109+71, 130)-Net over F₄ — Constructive and digital

Digital (109, 180, 130)-net over F₄, using

t-expansion [i] based on digital (105, 180, 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+71, 279)-Net over F₄ — Digital

Digital (109, 180, 279)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+71, 5533)-Net in Base 4 — Upper bound on s

There is no (109, 180, 5534)-net in base 4, because

1 times m-reduction [i] would yield (109, 179, 5534)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 588522 413014 371382 105664 006586 464106 772640 991659 120158 944750 454508 298855 843474 799350 140889 485470 494334 883320 > 4¹⁷⁹ [i]