MinT - Best Known (156−49, 156, s)-Nets in Base 4

Best Known (156−49, 156, s)-Nets in Base 4

(156−49, 156, 312)-Net over F₄ — Constructive and digital

Digital (107, 156, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 52, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(156−49, 156, 560)-Net over F₄ — Digital

Digital (107, 156, 560)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−49, 156, 25247)-Net in Base 4 — Upper bound on s

There is no (107, 156, 25248)-net in base 4, because

1 times m-reduction [i] would yield (107, 155, 25248)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2087 837218 846157 975954 768627 358460 251470 506532 039845 762106 616386 894357 749802 532423 970088 009791 > 4¹⁵⁵ [i]