MinT - Best Known (84−28, 84, s)-Nets in Base 4

Best Known (84−28, 84, s)-Nets in Base 4

(84−28, 84, 195)-Net over F₄ — Constructive and digital

Digital (56, 84, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 28, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(84−28, 84, 277)-Net over F₄ — Digital

Digital (56, 84, 277)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−28, 84, 8243)-Net in Base 4 — Upper bound on s

There is no (56, 84, 8244)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 374 495604 822093 336284 106486 774070 783389 719736 143860 > 4⁸⁴ [i]