MinT - Best Known (115−66, 115, s)-Nets in Base 4

Best Known (115−66, 115, s)-Nets in Base 4

(115−66, 115, 66)-Net over F₄ — Constructive and digital

Digital (49, 115, 66)-net over F₄, using

net from sequence [i] based on digital (49, 65)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
  - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(115−66, 115, 81)-Net over F₄ — Digital

Digital (49, 115, 81)-net over F₄, using

t-expansion [i] based on digital (46, 115, 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]

(115−66, 115, 523)-Net in Base 4 — Upper bound on s

There is no (49, 115, 524)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1784 081927 809917 187656 432161 278913 353823 715435 787521 487894 192828 120048 > 4¹¹⁵ [i]