MinT - Best Known (109, 109+93, s)-Nets in Base 4

Best Known (109, 109+93, s)-Nets in Base 4

(109, 109+93, 130)-Net over F₄ — Constructive and digital

Digital (109, 202, 130)-net over F₄, using

t-expansion [i] based on digital (105, 202, 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]

(109, 109+93, 188)-Net over F₄ — Digital

Digital (109, 202, 188)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+93, 2525)-Net in Base 4 — Upper bound on s

There is no (109, 202, 2526)-net in base 4, because

1 times m-reduction [i] would yield (109, 201, 2526)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 334403 501563 815823 164697 171271 163001 033988 444387 579385 610848 958421 817337 526967 392945 182293 780440 104639 557847 160752 568448 > 4²⁰¹ [i]