MinT - Best Known (122, 122+138, s)-Nets in Base 4

Best Known (122, 122+138, s)-Nets in Base 4

(122, 122+138, 130)-Net over F₄ — Constructive and digital

Digital (122, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 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]

(122, 122+138, 168)-Net over F₄ — Digital

Digital (122, 260, 168)-net over F₄, using

t-expansion [i] based on digital (115, 260, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(122, 122+138, 1585)-Net in Base 4 — Upper bound on s

There is no (122, 260, 1586)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 577008 045877 510632 235799 914194 564378 211709 709333 787150 151027 275220 045701 555869 083419 774440 041167 946482 255816 570922 176596 369203 683032 591663 418700 986190 309920 > 4²⁶⁰ [i]