MinT - Best Known (108, 108+150, s)-Nets in Base 4

Best Known (108, 108+150, s)-Nets in Base 4

(108, 108+150, 130)-Net over F₄ — Constructive and digital

Digital (108, 258, 130)-net over F₄, using

t-expansion [i] based on digital (105, 258, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(108, 108+150, 144)-Net over F₄ — Digital

Digital (108, 258, 144)-net over F₄, using

t-expansion [i] based on digital (91, 258, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(108, 108+150, 1067)-Net in Base 4 — Upper bound on s

There is no (108, 258, 1068)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 215744 585977 936796 703417 180355 531006 333556 827329 513713 045430 446990 070907 396602 530468 880192 144845 399322 460479 444657 998579 152947 511492 885781 916851 179068 891760 > 4²⁵⁸ [i]