MinT - Best Known (80, 80+178, s)-Nets in Base 4

Best Known (80, 80+178, s)-Nets in Base 4

(80, 80+178, 104)-Net over F₄ — Constructive and digital

Digital (80, 258, 104)-net over F₄, using

t-expansion [i] based on digital (73, 258, 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+178, 112)-Net over F₄ — Digital

Digital (80, 258, 112)-net over F₄, using

t-expansion [i] based on digital (73, 258, 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+178, 558)-Net in Base 4 — Upper bound on s

There is no (80, 258, 559)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 229587 752883 262732 132068 963578 835905 290989 745479 537661 124470 692720 334333 979224 938351 649106 897777 287717 123459 471348 791666 151131 441800 791716 453684 105588 673120 > 4²⁵⁸ [i]