MinT - Best Known (219−43, 219, s)-Nets in Base 4

Best Known (219−43, 219, s)-Nets in Base 4

(219−43, 219, 1539)-Net over F₄ — Constructive and digital

Digital (176, 219, 1539)-net over F₄, using

3 times m-reduction [i] based on digital (176, 222, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 74, 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]

(219−43, 219, 7606)-Net over F₄ — Digital

Digital (176, 219, 7606)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−43, 219, 5144296)-Net in Base 4 — Upper bound on s

There is no (176, 219, 5144297)-net in base 4, because

1 times m-reduction [i] would yield (176, 218, 5144297)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 177451 343960 488318 416981 137115 578630 176224 126373 707252 072697 290473 059927 249329 379841 212273 718588 732868 829748 660874 736951 930440 372352 > 4²¹⁸ [i]