MinT - Best Known (86, 86+38, s)-Nets in Base 4

Best Known (86, 86+38, s)-Nets in Base 4

(86, 86+38, 312)-Net over F₄ — Constructive and digital

Digital (86, 124, 312)-net over F₄, using

4¹ times duplication [i] based on digital (85, 123, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 41, 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]

(86, 86+38, 518)-Net over F₄ — Digital

Digital (86, 124, 518)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+38, 22440)-Net in Base 4 — Upper bound on s

There is no (86, 124, 22441)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 452 528365 894215 287975 145235 660562 645114 917180 221924 246334 143981 916897 568272 > 4¹²⁴ [i]