MinT - Best Known (206−99, 206, s)-Nets in Base 4

Best Known (206−99, 206, s)-Nets in Base 4

(206−99, 206, 130)-Net over F₄ — Constructive and digital

Digital (107, 206, 130)-net over F₄, using

t-expansion [i] based on digital (105, 206, 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]

(206−99, 206, 167)-Net over F₄ — Digital

Digital (107, 206, 167)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−99, 206, 2063)-Net in Base 4 — Upper bound on s

There is no (107, 206, 2064)-net in base 4, because

1 times m-reduction [i] would yield (107, 205, 2064)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2657 580856 383095 252876 718025 458077 623054 444653 044316 252388 752854 248983 118454 766430 921761 646758 578196 943333 672696 819576 762240 > 4²⁰⁵ [i]