MinT - Best Known (156−82, 156, s)-Nets in Base 4

Best Known (156−82, 156, s)-Nets in Base 4

(156−82, 156, 104)-Net over F₄ — Constructive and digital

Digital (74, 156, 104)-net over F₄, using

t-expansion [i] based on digital (73, 156, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(156−82, 156, 112)-Net over F₄ — Digital

Digital (74, 156, 112)-net over F₄, using

t-expansion [i] based on digital (73, 156, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(156−82, 156, 1017)-Net in Base 4 — Upper bound on s

There is no (74, 156, 1018)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8465 722417 239994 991335 216398 840187 276462 410264 246727 534126 696585 850828 791535 626479 725463 851965 > 4¹⁵⁶ [i]