MinT - Best Known (58, 58+97, s)-Nets in Base 4

Best Known (58, 58+97, s)-Nets in Base 4

(58, 58+97, 66)-Net over F₄ — Constructive and digital

Digital (58, 155, 66)-net over F₄, using

t-expansion [i] based on digital (49, 155, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(58, 58+97, 91)-Net over F₄ — Digital

Digital (58, 155, 91)-net over F₄, using

t-expansion [i] based on digital (50, 155, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(58, 58+97, 495)-Net in Base 4 — Upper bound on s

There is no (58, 155, 496)-net in base 4, because

1 times m-reduction [i] would yield (58, 154, 496)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 557 761285 607059 316675 493757 515304 982474 071756 706588 897978 176600 131960 113799 267342 974916 008764 > 4¹⁵⁴ [i]