MinT - Best Known (245−116, 245, s)-Nets in Base 4

Best Known (245−116, 245, s)-Nets in Base 4

(245−116, 245, 130)-Net over F₄ — Constructive and digital

Digital (129, 245, 130)-net over F₄, using

t-expansion [i] based on digital (105, 245, 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]

(245−116, 245, 204)-Net over F₄ — Digital

Digital (129, 245, 204)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−116, 245, 2566)-Net in Base 4 — Upper bound on s

There is no (129, 245, 2567)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3239 083870 003750 284435 529671 871145 875161 676596 564743 130262 647484 280872 949655 727647 382163 791656 838777 315363 708946 604460 831134 582628 496354 175364 005952 > 4²⁴⁵ [i]