MinT - Best Known (202, 202+56, s)-Nets in Base 4

Best Known (202, 202+56, s)-Nets in Base 4

(202, 202+56, 1539)-Net over F₄ — Constructive and digital

Digital (202, 258, 1539)-net over F₄, using

t-expansion [i] based on digital (200, 258, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 86, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(202, 202+56, 4772)-Net over F₄ — Digital

Digital (202, 258, 4772)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(202, 202+56, 1328706)-Net in Base 4 — Upper bound on s

There is no (202, 258, 1328707)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214526 782797 302920 738918 897639 496845 128383 674130 894619 336807 945985 405706 167022 645553 798842 984055 388189 036321 204363 729125 357277 048761 460947 060457 497602 488624 > 4²⁵⁸ [i]