MinT - Best Known (210−88, 210, s)-Nets in Base 4

Best Known (210−88, 210, s)-Nets in Base 4

(210−88, 210, 130)-Net over F₄ — Constructive and digital

Digital (122, 210, 130)-net over F₄, using

t-expansion [i] based on digital (105, 210, 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]

(210−88, 210, 263)-Net over F₄ — Digital

Digital (122, 210, 263)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−88, 210, 4261)-Net in Base 4 — Upper bound on s

There is no (122, 210, 4262)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 708213 977298 379681 413689 183690 104745 837750 831184 785904 078416 694851 870968 543223 033091 794050 777762 241353 974017 475232 122410 367440 > 4²¹⁰ [i]