MinT - Best Known (88, 88+42, s)-Nets in Base 4

Best Known (88, 88+42, s)-Nets in Base 4

(88, 88+42, 240)-Net over F₄ — Constructive and digital

Digital (88, 130, 240)-net over F₄, using

4¹ times duplication [i] based on digital (87, 129, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 43, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(88, 88+42, 433)-Net over F₄ — Digital

Digital (88, 130, 433)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+42, 15414)-Net in Base 4 — Upper bound on s

There is no (88, 130, 15415)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 853807 653609 276048 620461 747818 163147 280276 968224 354730 371924 329546 121862 556226 > 4¹³⁰ [i]