MinT - Best Known (120, 120+81, s)-Nets in Base 4

Best Known (120, 120+81, s)-Nets in Base 4

(120, 120+81, 130)-Net over F₄ — Constructive and digital

Digital (120, 201, 130)-net over F₄, using

t-expansion [i] based on digital (105, 201, 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]

(120, 120+81, 286)-Net over F₄ — Digital

Digital (120, 201, 286)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 120+81, 5349)-Net in Base 4 — Upper bound on s

There is no (120, 201, 5350)-net in base 4, because

1 times m-reduction [i] would yield (120, 200, 5350)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 590570 785067 991364 074409 822443 720061 307658 431594 737325 311704 173775 766207 503914 892121 576974 690992 777087 712921 893596 935368 > 4²⁰⁰ [i]