MinT - Best Known (80, 80+164, s)-Nets in Base 4

Best Known (80, 80+164, s)-Nets in Base 4

(80, 80+164, 104)-Net over F₄ — Constructive and digital

Digital (80, 244, 104)-net over F₄, using

t-expansion [i] based on digital (73, 244, 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+164, 112)-Net over F₄ — Digital

Digital (80, 244, 112)-net over F₄, using

t-expansion [i] based on digital (73, 244, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(80, 80+164, 581)-Net in Base 4 — Upper bound on s

There is no (80, 244, 582)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 902 636645 427192 617574 286344 423550 943338 011252 153320 427885 597496 012581 374825 872474 060423 283935 470410 142597 452265 366690 178487 594251 658687 414115 739840 > 4²⁴⁴ [i]