MinT - Best Known (175−55, 175, s)-Nets in Base 4

Best Known (175−55, 175, s)-Nets in Base 4

(175−55, 175, 312)-Net over F₄ — Constructive and digital

Digital (120, 175, 312)-net over F₄, using

4¹ times duplication [i] based on digital (119, 174, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 58, 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]

(175−55, 175, 614)-Net over F₄ — Digital

Digital (120, 175, 614)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−55, 175, 27598)-Net in Base 4 — Upper bound on s

There is no (120, 175, 27599)-net in base 4, because

1 times m-reduction [i] would yield (120, 174, 27599)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 573 788667 143951 352401 036529 689586 127768 187784 819499 168975 198712 489323 669953 227392 092272 537346 468355 538560 > 4¹⁷⁴ [i]