MinT - Best Known (226−46, 226, s)-Nets in Base 4

Best Known (226−46, 226, s)-Nets in Base 4

(226−46, 226, 1539)-Net over F₄ — Constructive and digital

Digital (180, 226, 1539)-net over F₄, using

2 times m-reduction [i] based on digital (180, 228, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 76, 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]

(226−46, 226, 6227)-Net over F₄ — Digital

Digital (180, 226, 6227)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−46, 226, 2589558)-Net in Base 4 — Upper bound on s

There is no (180, 226, 2589559)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11629 473971 786829 457622 010196 139629 966161 167748 429282 275046 604371 444124 095252 432481 866810 516924 857330 662494 365831 090541 425276 742705 145588 > 4²²⁶ [i]