MinT - Best Known (80, 80+69, s)-Nets in Base 4

Best Known (80, 80+69, s)-Nets in Base 4

(80, 80+69, 104)-Net over F₄ — Constructive and digital

Digital (80, 149, 104)-net over F₄, using

t-expansion [i] based on digital (73, 149, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(80, 80+69, 142)-Net over F₄ — Digital

Digital (80, 149, 142)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+69, 1856)-Net in Base 4 — Upper bound on s

There is no (80, 149, 1857)-net in base 4, because

1 times m-reduction [i] would yield (80, 148, 1857)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 128828 400355 800600 700613 034544 808192 394274 821901 762115 615011 877120 081866 481103 912650 910208 > 4¹⁴⁸ [i]