MinT - Best Known (108, 108+93, s)-Nets in Base 4

Best Known (108, 108+93, s)-Nets in Base 4

(108, 108+93, 130)-Net over F₄ — Constructive and digital

Digital (108, 201, 130)-net over F₄, using

t-expansion [i] based on digital (105, 201, 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+93, 184)-Net over F₄ — Digital

Digital (108, 201, 184)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+93, 2449)-Net in Base 4 — Upper bound on s

There is no (108, 201, 2450)-net in base 4, because

1 times m-reduction [i] would yield (108, 200, 2450)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 588403 370262 011782 884799 982250 469285 030523 673005 092054 950640 901458 796874 546637 847959 404615 459286 920027 151321 544084 460320 > 4²⁰⁰ [i]