MinT - Best Known (111, 111+84, s)-Nets in Base 4

Best Known (111, 111+84, s)-Nets in Base 4

(111, 111+84, 130)-Net over F₄ — Constructive and digital

Digital (111, 195, 130)-net over F₄, using

t-expansion [i] based on digital (105, 195, 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]

(111, 111+84, 225)-Net over F₄ — Digital

Digital (111, 195, 225)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+84, 3400)-Net in Base 4 — Upper bound on s

There is no (111, 195, 3401)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2525 174158 066468 686178 661403 152753 814038 568964 262692 915977 180659 771332 942397 128173 307218 366284 190347 700563 434264 761088 > 4¹⁹⁵ [i]