MinT - Best Known (55, 78, s)-Nets in Base 4

Best Known (55, 78, s)-Nets in Base 4

(55, 78, 312)-Net over F₄ — Constructive and digital

Digital (55, 78, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 26, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(55, 78, 422)-Net over F₄ — Digital

Digital (55, 78, 422)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 78, 26802)-Net in Base 4 — Upper bound on s

There is no (55, 78, 26803)-net in base 4, because

1 times m-reduction [i] would yield (55, 77, 26803)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 22842 299103 059994 064663 558465 993125 634314 253000 > 4⁷⁷ [i]