MinT - Best Known (202−57, 202, s)-Nets in Base 4

Best Known (202−57, 202, s)-Nets in Base 4

(202−57, 202, 531)-Net over F₄ — Constructive and digital

Digital (145, 202, 531)-net over F₄, using

5 times m-reduction [i] based on digital (145, 207, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 69, 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]

(202−57, 202, 1088)-Net over F₄ — Digital

Digital (145, 202, 1088)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−57, 202, 79011)-Net in Base 4 — Upper bound on s

There is no (145, 202, 79012)-net in base 4, because

1 times m-reduction [i] would yield (145, 201, 79012)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 331730 988496 988554 683506 556066 819325 279684 404103 853003 289220 049550 048226 142009 130996 815256 816532 348049 087400 635594 469192 > 4²⁰¹ [i]