MinT - Best Known (248−60, 248, s)-Nets in Base 4

Best Known (248−60, 248, s)-Nets in Base 4

(248−60, 248, 1036)-Net over F₄ — Constructive and digital

Digital (188, 248, 1036)-net over F₄, using

trace code for nets [i] based on digital (2, 62, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(248−60, 248, 2611)-Net over F₄ — Digital

Digital (188, 248, 2611)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−60, 248, 380775)-Net in Base 4 — Upper bound on s

There is no (188, 248, 380776)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 204598 688014 143716 107909 822969 309155 869078 735685 506666 877766 575559 783494 402528 938409 673128 795162 477369 996010 621076 975116 957069 616214 817557 900896 381188 > 4²⁴⁸ [i]