MinT - Best Known (123, 123+85, s)-Nets in Base 4

Best Known (123, 123+85, s)-Nets in Base 4

(123, 123+85, 130)-Net over F₄ — Constructive and digital

Digital (123, 208, 130)-net over F₄, using

t-expansion [i] based on digital (105, 208, 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+85, 282)-Net over F₄ — Digital

Digital (123, 208, 282)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+85, 5070)-Net in Base 4 — Upper bound on s

There is no (123, 208, 5071)-net in base 4, because

1 times m-reduction [i] would yield (123, 207, 5071)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42530 866517 473714 911929 463480 674803 101308 379830 272044 786595 494040 007485 064145 331693 245958 659569 419498 527832 586911 582045 645330 > 4²⁰⁷ [i]