MinT - Best Known (118−72, 118, s)-Nets in Base 4

Best Known (118−72, 118, s)-Nets in Base 4

(118−72, 118, 56)-Net over F₄ — Constructive and digital

Digital (46, 118, 56)-net over F₄, using

t-expansion [i] based on digital (33, 118, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(118−72, 118, 81)-Net over F₄ — Digital

Digital (46, 118, 81)-net over F₄, using

net from sequence [i] based on digital (46, 80)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 46 and N(F) ≥ 81, using
  - Drinfeld modules of rank 1 [i]

(118−72, 118, 418)-Net in Base 4 — Upper bound on s

There is no (46, 118, 419)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 110694 272683 511320 833333 751172 781474 393226 610475 342321 638497 393896 166720 > 4¹¹⁸ [i]