MinT - Best Known (253−120, 253, s)-Nets in Base 4

Best Known (253−120, 253, s)-Nets in Base 4

(253−120, 253, 130)-Net over F₄ — Constructive and digital

Digital (133, 253, 130)-net over F₄, using

t-expansion [i] based on digital (105, 253, 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]

(253−120, 253, 209)-Net over F₄ — Digital

Digital (133, 253, 209)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(253−120, 253, 2623)-Net in Base 4 — Upper bound on s

There is no (133, 253, 2624)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 213 073989 158299 881518 229500 344898 885151 718109 098267 129985 885050 575708 776026 191362 709265 028783 900812 660815 489122 315504 011016 708118 259086 530712 453457 496911 > 4²⁵³ [i]