MinT - Best Known (99, 99+79, s)-Nets in Base 4

Best Known (99, 99+79, s)-Nets in Base 4

(99, 99+79, 130)-Net over F₄ — Constructive and digital

Digital (99, 178, 130)-net over F₄, using

8 times m-reduction [i] based on digital (99, 186, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 93, 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]

(99, 99+79, 189)-Net over F₄ — Digital

Digital (99, 178, 189)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+79, 2739)-Net in Base 4 — Upper bound on s

There is no (99, 178, 2740)-net in base 4, because

1 times m-reduction [i] would yield (99, 177, 2740)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36831 498583 214469 986214 846548 277698 062018 705614 914454 919863 787031 891399 160458 117602 799577 235784 723724 881668 > 4¹⁷⁷ [i]