MinT - Best Known (116, 165, s)-Nets in Base 4

Best Known (116, 165, s)-Nets in Base 4

(116, 165, 384)-Net over F₄ — Constructive and digital

Digital (116, 165, 384)-net over F₄, using

t-expansion [i] based on digital (115, 165, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 55, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(116, 165, 739)-Net over F₄ — Digital

Digital (116, 165, 739)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 165, 42473)-Net in Base 4 — Upper bound on s

There is no (116, 165, 42474)-net in base 4, because

1 times m-reduction [i] would yield (116, 164, 42474)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 546 945029 619661 659023 109109 452621 622312 139494 937701 786994 240944 098171 157383 625844 950005 780034 498174 > 4¹⁶⁴ [i]