MinT - Best Known (202−49, 202, s)-Nets in Base 3

Best Known (202−49, 202, s)-Nets in Base 3

(202−49, 202, 400)-Net over F₃ — Constructive and digital

Digital (153, 202, 400)-net over F₃, using

3² times duplication [i] based on digital (151, 200, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 50, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(202−49, 202, 967)-Net over F₃ — Digital

Digital (153, 202, 967)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−49, 202, 48530)-Net in Base 3 — Upper bound on s

There is no (153, 202, 48531)-net in base 3, because

1 times m-reduction [i] would yield (153, 201, 48531)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 797114 803796 236165 909546 042366 087338 021230 349079 145821 391429 575630 294787 581592 106326 747446 859217 > 3²⁰¹ [i]