MinT - Best Known (93, 93+42, s)-Nets in Base 4

Best Known (93, 93+42, s)-Nets in Base 4

(93, 93+42, 312)-Net over F₄ — Constructive and digital

Digital (93, 135, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 45, 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]

(93, 93+42, 519)-Net over F₄ — Digital

Digital (93, 135, 519)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+42, 21449)-Net in Base 4 — Upper bound on s

There is no (93, 135, 21450)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1898 448020 063475 316629 717038 186988 202074 517653 634728 889536 332470 745262 361955 774536 > 4¹³⁵ [i]