MinT - Best Known (150−67, 150, s)-Nets in Base 4

Best Known (150−67, 150, s)-Nets in Base 4

(150−67, 150, 130)-Net over F₄ — Constructive and digital

Digital (83, 150, 130)-net over F₄, using

4 times m-reduction [i] based on digital (83, 154, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 77, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(150−67, 150, 160)-Net over F₄ — Digital

Digital (83, 150, 160)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−67, 150, 2267)-Net in Base 4 — Upper bound on s

There is no (83, 150, 2268)-net in base 4, because

1 times m-reduction [i] would yield (83, 149, 2268)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 514502 247716 692629 000170 540335 596434 781647 926583 144239 270355 609395 635532 591137 289749 320950 > 4¹⁴⁹ [i]