MinT - Best Known (250−52, 250, s)-Nets in Base 4

Best Known (250−52, 250, s)-Nets in Base 4

(250−52, 250, 1539)-Net over F₄ — Constructive and digital

Digital (198, 250, 1539)-net over F₄, using

5 times m-reduction [i] based on digital (198, 255, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 85, 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]

(250−52, 250, 5941)-Net over F₄ — Digital

Digital (198, 250, 5941)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−52, 250, 2163744)-Net in Base 4 — Upper bound on s

There is no (198, 250, 2163745)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 273422 512167 842479 457086 742787 858745 331477 793261 757559 162020 281105 353747 628199 912194 207240 735023 329879 715957 526253 898090 791000 731995 969410 172439 214096 > 4²⁵⁰ [i]