MinT - Best Known (123, 123+82, s)-Nets in Base 4

Best Known (123, 123+82, s)-Nets in Base 4

(123, 123+82, 130)-Net over F₄ — Constructive and digital

Digital (123, 205, 130)-net over F₄, using

t-expansion [i] based on digital (105, 205, 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]

(123, 123+82, 299)-Net over F₄ — Digital

Digital (123, 205, 299)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+82, 5475)-Net in Base 4 — Upper bound on s

There is no (123, 205, 5476)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2651 104465 105082 378504 501432 614856 521758 723344 151344 576766 383557 530010 700846 626768 376231 821056 080379 401343 568541 495319 774856 > 4²⁰⁵ [i]