MinT - Best Known (91−77, 91, s)-Nets in Base 64

Best Known (91−77, 91, s)-Nets in Base 64

(91−77, 91, 177)-Net over F₆₄ — Constructive and digital

Digital (14, 91, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 91, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(91−77, 91, 257)-Net over F₆₄ — Digital

Digital (14, 91, 257)-net over F₆₄, using

t-expansion [i] based on digital (12, 91, 257)-net over F₆₄, using
- net from sequence [i] based on digital (12, 256)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 12 and N(F) ≥ 257, using
    - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

(91−77, 91, 4502)-Net in Base 64 — Upper bound on s

There is no (14, 91, 4503)-net in base 64, because

1 times m-reduction [i] would yield (14, 90, 4503)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 624937 329598 570197 737051 163610 819074 177780 520532 395168 947296 806977 899599 692494 946881 984278 468129 807831 337393 021349 289265 702747 073800 959064 972137 479983 317804 174060 > 64⁹⁰ [i]