MinT - Best Known (68, 68+28, s)-Nets in Base 4

Best Known (68, 68+28, s)-Nets in Base 4

(68, 68+28, 312)-Net over F₄ — Constructive and digital

Digital (68, 96, 312)-net over F₄, using

t-expansion [i] based on digital (67, 96, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 32, 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]

(68, 68+28, 517)-Net over F₄ — Digital

Digital (68, 96, 517)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+28, 27075)-Net in Base 4 — Upper bound on s

There is no (68, 96, 27076)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6280 278904 057411 644176 337356 127369 211839 610842 658968 436336 > 4⁹⁶ [i]