MinT - Best Known (187−80, 187, s)-Nets in Base 4

Best Known (187−80, 187, s)-Nets in Base 4

(187−80, 187, 130)-Net over F₄ — Constructive and digital

Digital (107, 187, 130)-net over F₄, using

t-expansion [i] based on digital (105, 187, 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]

(187−80, 187, 222)-Net over F₄ — Digital

Digital (107, 187, 222)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−80, 187, 3397)-Net in Base 4 — Upper bound on s

There is no (107, 187, 3398)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38777 792844 412570 489153 247351 475223 632363 298273 800661 129569 598955 340008 197545 828514 274421 045206 686537 691435 255224 > 4¹⁸⁷ [i]