MinT - Best Known (88−26, 88, s)-Nets in Base 4

Best Known (88−26, 88, s)-Nets in Base 4

(88−26, 88, 312)-Net over F₄ — Constructive and digital

Digital (62, 88, 312)-net over F₄, using

4¹ times duplication [i] based on digital (61, 87, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 29, 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]

(88−26, 88, 459)-Net over F₄ — Digital

Digital (62, 88, 459)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−26, 88, 22468)-Net in Base 4 — Upper bound on s

There is no (62, 88, 22469)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 95825 277166 544562 155010 508208 288393 907738 083061 782560 > 4⁸⁸ [i]