MinT - Best Known (205−57, 205, s)-Nets in Base 4

Best Known (205−57, 205, s)-Nets in Base 4

(205−57, 205, 531)-Net over F₄ — Constructive and digital

Digital (148, 205, 531)-net over F₄, using

t-expansion [i] based on digital (147, 205, 531)-net over F₄, using
- 5 times m-reduction [i] based on digital (147, 210, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 70, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(205−57, 205, 1176)-Net over F₄ — Digital

Digital (148, 205, 1176)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−57, 205, 91666)-Net in Base 4 — Upper bound on s

There is no (148, 205, 91667)-net in base 4, because

1 times m-reduction [i] would yield (148, 204, 91667)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 661 069548 350374 754383 300218 615252 343653 041645 339431 273104 807626 053213 279220 316348 350362 566549 430958 806145 578140 380140 829056 > 4²⁰⁴ [i]