MinT - Best Known (228−45, 228, s)-Nets in Base 4

Best Known (228−45, 228, s)-Nets in Base 4

(228−45, 228, 1539)-Net over F₄ — Constructive and digital

Digital (183, 228, 1539)-net over F₄, using

t-expansion [i] based on digital (182, 228, 1539)-net over F₄, using
- 3 times m-reduction [i] based on digital (182, 231, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 77, 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]

(228−45, 228, 7600)-Net over F₄ — Digital

Digital (183, 228, 7600)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−45, 228, 4919201)-Net in Base 4 — Upper bound on s

There is no (183, 228, 4919202)-net in base 4, because

1 times m-reduction [i] would yield (183, 227, 4919202)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46517 685057 555668 568060 106951 578430 139142 219263 887614 487120 454329 030839 157376 914919 989668 903115 262553 543183 655512 409174 459065 233043 641680 > 4²²⁷ [i]