MinT - Best Known (109, 109+94, s)-Nets in Base 4

Best Known (109, 109+94, s)-Nets in Base 4

(109, 109+94, 130)-Net over F₄ — Constructive and digital

Digital (109, 203, 130)-net over F₄, using

t-expansion [i] based on digital (105, 203, 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+94, 185)-Net over F₄ — Digital

Digital (109, 203, 185)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+94, 2401)-Net in Base 4 — Upper bound on s

There is no (109, 203, 2402)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 167 103017 147638 839194 346578 384571 950484 129928 590230 558098 793813 837054 926078 129132 801234 090843 424472 607648 569750 035019 547360 > 4²⁰³ [i]